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FLOCKING AND PATTERN MOTION IN A MODIFIED CUCKER-SMALE MODEL

  • Li, Xiang (College of Science National University of Defense Technology) ;
  • Liu, Yicheng (College of Science National University of Defense Technology) ;
  • Wu, Jun (College of Mathematics and Computer Science Changsha University of Science Technology)
  • Received : 2015.08.06
  • Published : 2016.09.30

Abstract

Self-organizing systems arise very naturally in artificial intelligence, and in physical, biological and social sciences. In this paper, we modify the classic Cucker-Smale model at both microscopic and macroscopic levels by taking the target motion pattern driving forces into consideration. Such target motion pattern driving force functions are properly defined for the line-shaped motion pattern and the ball-shaped motion pattern. For the modified Cucker-Smale model with the prescribed line-shaped motion pattern, we have analytically shown that there is a flocking pattern with an asymptotic flocking velocity. This is illustrated by numerical simulations using both symmetric and non-symmetric pairwise influence functions. For the modified Cucker-Smale model with the prescribed ball-shaped motion pattern, our simulations suggest that the solution also converges to the prescribed motion pattern.

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